If f : R → R and g : R &r

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 Multiple Choice QuestionsMultiple Choice Questions

61.

Let A = x  R, x  0, - 4  x  4 and f : A  R defined by f(x) = xx for x  A. Then, the range of f is

  • {1, - 1}

  • x : 0  x  1

  • (1)

  • x : - 4 x  0


62.

If log2 = a, log3 = b, log7 = c and 6x = 7x + 4 then x is equal to

  • 4bc + a - b

  • 4ca + b - c

  • 4cc - a - b

  • 4aa + b - c


63.

In the sequence, (1, 2, 3), (4, 5, 6), (7, 8, 9, 10)... of sets, the sum of elements in the 50th set is

  • 62525

  • 65225

  • 56255

  • 55765


64.

1 + xlogea + x22!logea2 + x33!logea3 + ...a > 0, x  R, is equal to

  • ax

  • ax

  • alogex

  • x


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65.

If f : R  R and g : R  R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(x) = x2 + 7, then values ofx such that g(f(x)) = 8 are

  • 1, 2

  • - 1, 2

  • - 1, - 2

  • 1, - 2


C.

- 1, - 2

We have, fx = 2x + 3, gx = x2 + 7gfx = g2x + 3 = 2x + 32 + 7 = 8 4x2 + 9 + 12x + 7 = 8 4x2 + 12x + 8 = 0     x2 + 3x + 2 = 0 x + 1x + 2 = 0                       x = - 1, - 2


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66.

Suppose f : [- 2, 2]  R is defined by

fx = - 1,                              for - 2  x  0x - 1,                           for 0  x  2x  - 2, 2 : x  0 and fx = x

is equal to

  • {- 1}

  • 0

  • - 12

  • ϕ


67.

If f : R  R and g :R  R are given by f(x) = x and g(x) = [x] for each x  R, then x  R : gfx  fgx is equal to

  • Z  - , 0

  • - , 0

  • Z

  • R


68.

If f(x) = 1x + 22x - 4 + 1x - 22x - 4 for x > 2, then f(11) is equal to

  • 76

  • 56

  • 67

  • 57


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69.

If efx = 10 + x10 - x, x  - 10, 10 and f(x) = kf200x100 + x2, then k is equal to

  • 0.5

  • 0.6

  • 0.7

  • 0.8


70.

Let a, b, and c be such that 11 - x1 - 2x1 - 3x = a1 - x + b1 - 2x + c1 - 3x then, a1 + b3 + c5 is equal to

  • 115

  • 16

  • 15

  • 13


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